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The rapid expansion of social media platforms has provided unprecedented access to massive amounts of multimodal user-generated content. Comprehending user emotions can provide valuable insights for improving communication and understanding of human behaviors. Despite significant advancements in Affective Computing, the diverse factors influencing user emotions in social networks remain relatively understudied. Moreover, there is a notable lack of deep learning-based methods for predicting user emotions in social networks, which could be addressed by leveraging the extensive multimodal data available. This work presents a novel formulation of personalized emotion prediction in social networks based on heterogeneous graph learning. Building upon this formulation, we design HMG-Emo, a Heterogeneous Multimodal Graph Learning Framework that utilizes deep learning-based features for user emotion recognition. Additionally, we include a dynamic context fusion module in HMG-Emo that is capable of adaptively integrating the different modalities in social media data. Through extensive experiments, we demonstrate the effectiveness of HMG-Emo and verify the superiority of adopting a graph neural network-based approach, which outperforms existing baselines that use rich hand-crafted features. To the best of our knowledge, HMG-Emo is the first multimodal and deep-learning-based approach to predict personalized emotions within online social networks. Our work highlights the significance of exploiting advanced deep learning techniques for less-explored problems in Affective Computing.